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Miroslav Krstic

For transformational contributions in PDE control, nonlinear delay systems, extremum seeking, adaptive control, stochastic nonlinear stabilization. And their industrial applications

Miroslav Krstic is Distinguished Professor of Mechanical and Aerospace Engineering, holds the Alspach endowed chair, and is the founding director of the Center for Control Systems and Dynamics at UC San Diego. He also serves as Senior Associate Vice Chancellor for Research at UCSD. As a graduate student, Krstic won the UC Santa Barbara best dissertation award and student best paper awards at CDC and ACC. Krstic has been elected Fellow of IEEE, IFAC, ASME, SIAM, AAAS, IET (UK), and AIAA (Assoc. Fellow), as well as foreign member of the Serbian Academy of Sciences and Arts, and of the Academy of Engineering of Serbia. He has received the SIAM Reid Prize, ASME Oldenburger Medal, Nyquist Lecture Prize, Paynter Outstanding Investigator Award, Ragazzini Education Award, IFAC Nonlinear Control Systems Award, Chestnut textbook prize, Control Systems Society Distinguished Member Award, the PECASE, NSF Career, and ONR Young Investigator awards, the Schuck (’96 and ’19) and Axelby paper prizes, and the first UCSD Research Award given to an engineer. Krstic has held the Springer Visiting Professorship at UC Berkeley, the Distinguished Visiting Fellowship of the Royal Academy of Engineering, the Invitation Fellowship of the Japan Society for the Promotion of Science, and has been awarded four honorary professorships outside of the United States. He serves as Editor-in-Chief of Systems & Control Letters and Editor in Automatica, has served as Senior Editor in IEEE Transactions on Automatic Control, and is editor of two Springer book series. He has served as Vice President for Technical Activities and BoG member of the IEEE Control Systems Society and, for a triennium, as chair of the IEEE CSS Fellow Committee. Krstic has coauthored fifteen books on adaptive, nonlinear, and stochastic control, extremum seeking, control of PDE systems including turbulent flows, and control of delay systems.

Text of Acceptance Speech: 

Dear Automatic Control colleagues,

I am happy and humbled to receive the Bellman Award.

My profound gratitude goes to the colleagues who supported my nomination. I am thankful and deeply moved by the selection committee and the A2C2, which advanced a candidate in his mid-fifties, an adolescent by Bellman award standards.

The timing of this award, which recognizes the achievement of an American control systems researcher, carries significance for me. The Bellman award came in the year that happened to be the thirtieth anniversary of my coming to the United States as a graduate student.

It is customary on this occasion for the recipient to say a few words about their formative years and professional trajectory.

I was born and grew up in a small city called Pirot, in remote southeastern Serbia. I was fortunate that my provincial city had one of the top science high schools in former Yugoslavia. And my caring parents spared no expense to provide my brother and me with broader cultural opportunities than those that our hometown could offer.

My undergraduate years at the Department of Electrical Engineering of the University of Belgrade provided me with two things. First, the toughest academic competition I’ve experienced, before or since, was during those five undergraduate years. And, second, I met my future wife in our freshman math class.

Before Petar Kokotovic gave me a PhD opportunity, I had only an inkling that I might have a shot at some success in research. But, within a few weeks of arriving in Santa Barbara, I had the fortune of solving a problem that had a reputation of being unsolvable, though I didn’t know that. So things moved quickly with research from that point on, and I had Petar’s unlimited attention. I could fill hours on being mentored by Petar. But let me just say that, during those Santa Barbara years, Petar’s enthusiasm and support for my work left me feeling that there was nothing more important happening in the world than what I was doing in research. At the same time, with everything I would produce or say, I had the training benefit of a keener, more unforgiving, and yet more nuanced critique than I would ever subsequently encounter, as a researcher or academic administrator.

Of the areas credited to me, the ones that probably come to mind first are PDE backstepping and extremum seeking. Let me describe how these interests started, soon after I left Santa Barbara.

Petar Kokotovic, Richard Murray, and Art Krener had a large project on controlling flow instabilities in jet engines. We solved those problems using reduced-order nonlinear ODE models of those flows. And it was clear that, for a nonlinear control researcher, there was hardly a more fertile ground than fluids. The only problem was: who would provide an ODE reduction for me for the next control design problem I tackle? If fluids people spend their entire careers refining, for a specific type of flow, the reductions from the Navier-Stokes representation to ODEs, it was obvious I could not count on them for control-oriented reduced models. I had to roll up my sleeves and build control methods directly for PDEs. From scratch. Because Riccati equations—in infinite dimension to boot—are not the way to extend PDE control to the nonlinear case. The answer to the challenge of constructive PDE control came in the form of continuum backstepping transformations, employing Volterra operators and easy-to-solve Goursat-form PDEs for the control gain functions. If you have interest in an example of this line of PDE control research, I recommend the paper with Coron, Bastin, and my student Vazquez, which has enabled stabilization of traffic flows in a congested, stop-and-go regime.

How I got drawn to extremum seeking is also interesting. In 1997, a combustion colleague at Maryland pointed me to publications from the 1940s and 1950s on what I would describe as an approach to adaptive control for nonlinear systems. Heuristic, but orders of magnitude simpler than what I had written my PhD on. Attempts at sleep were futile, for several days, until I figured out how to prove stability of this algorithm, using a combination of averaging and singular perturbation theorems. If you wanted to sample one control paper from the last quarter century on extremum seeking, I recommend the one on model-free seeking of Nash equilibria with Tamer Basar and my student Paul Frihauf.

To my students and collaborators, I would like to say: this Bellman award is yours. For your papers, books, theorems, and industrial products.

As I mention students, I want to extend gratitude to two companies that have been the environments in which my former students have been able to thrive and leave a legacy. At ASML, control of extreme ultraviolet photolithography has improved the density of microchips by 2-3 orders of magnitude. At General Atomics, control of aircraft arrestment on carriers has enabled one of the most impressive and deployed recent advances in defense technology.

I won’t pretend that it is not a delight to see my name in the list of the 44 recipients of the Bellman award. Scholars of incredible depth and engineers of stunning impact. I’ve studied the list. Amazingly, the numbers of American-born and foreign-born recipients of this US award seem to be the same: 22 each. If you sought an example of how the US is unequaled in extending opportunity to scientific immigrants, like myself, you could hardly find a clearer illustration.

It was also impossible for me to miss in the list that, after India, represented by four Bellman awardees, the second most highly represented foreign country is a certain little country, just a few percent more populous than the city of Atlanta, the country from which Petar Kokotovic, Drago Šiljak, and I came to the US. If I don’t mention this, in the hope of inspiring a few young minds at the Universities of Belgrade, Novi Sad, or Niš, who should?

I couldn’t have made it here without role models and without pioneers who charted the pathways along which it was then not that hard for me to walk. Among them are people who have also generously supported me over the years: Tamer Basar, Manfred Morari, Art Krener, Eduardo Sontag, Masayoshi Tomizuka, Galip Ulsoy, Jason Speyer, Graham Goodwin, Jean-Michel Coron, Petros Ioannou—to limit myself to ten. I hope that, in the remainder of my research career, I more fully deserve their support, as well as by other friends I don’t mention here but who are aware of the extent of my gratitude and respect.

Let me close and thank you with a quote from my former department chair who astutely observed: “To you guys, in control systems, every other field is a special case of control theory.”

What if that’s true?

June 7, 2022

Atlanta, GA USA

ACC 2022